Multi-Dimensional and Vorticity Effects in Inclined Shallow Water Flow

Indiana University, Bloomington IN

Investigators

Abstract

Hydraulic shocks and roll waves can drastically affect inclined shallow-water flow, which is particularly important to canal and dam spillway design. The Principal Investigator (PI) will use theoretical and computational methods to study the effects of rotational and multi-dimensions on the existence and stability of flow patterns in inclined shallow water flow. The results are expected be of interest to hydraulic engineers seeking to prevent damage from anomalous large waves, either by preventing their appearance, or by building remediating structures to a size and strength called for by the existing and developing theory. The PI will study a selection of novel problems on stability and behavior of inclined shallow water flow. The objective of the project is the incorporation of previously unaccounted multi-dimensional and rotational (vorticity) effects in the study of stability and behavior of roll waves and hydraulic shocks in a hydrodynamic engineering setting, to obtain comprehensive stability diagrams across all parameters. The project involves applicable and nonstandard mathematical issues addressing challenging problems from physical applications. For example, successful treatment of multidimensional shock and roll waves would advance general theory, while providing a solid framework on roll wave behavior in shallow water flow/hydraulic engineering. The research methods that will be used in the project include a blend of numerical, formal asymptotic, and dynamical systems/turning point tools with specialized techniques coming from detonation theory and hyperbolic conservation laws. The validation of simple stability criteria for roll waves in shallow water flow and the introduction of new asymptotic and numerical methods are of wider application in both hydraulic engineering and the theory of hyperbolic shock and boundary value problems. Likewise, the computation of all-parameters stability diagrams for commonly occurring flows is of basic foundational scientific interest. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.